The filter loss is zero if the burst waveform consists of a pure sinusoid at the designated
intermediate frequency. It is also very near zero as long as most of the burst energy is
confined within the passband of the RVP900 filter. The filter loss increases as the bandwidth
of the burst waveform increases and begins to spill out of that passband. Typical losses for a
well-matched filter are in the 0.5 dB ... 1.8 dB range, depending on the FIR length and other
design criteria.
For example, consider how the RVP900 filters would respond to a simple rectangular pulse
of energy lasting T
o
seconds. For this discussion we can ignore the sinusoidal IF carrier that
must also be present within the pulse, and just focus on the rectangular envelope. This is
valid because the signal bandwidth, and hence the
filter loss, is determined by the shape of
the modulation envelope. For a pulse of length T
o
to have unit-energy it must have an
amplitude of :
1
0
By centering this pulse at time zero the power spectrum is easily computed using a real-
valued integral:
=
0
2
0
2
1
0
cos
2
2
=
sin
2
2
2
0
where f is the frequency in Hz. This is the familiar "synch" function, whose main frequency
lobe extends from 1/T
o
to 1/T
o
Hz, and whose total power integrated over all frequencies
is 1.0.
We can now examine what the filter loss (dB
loss
) would be if this pulse were applied to a
band pass filter. The filter loss is the ratio of the power that is passed by the filter, divided by
the total input power (1.0 in this case). Assume for the moment that the filter is an ideal
band pass
filter centered at zero Hertz (corresponding to how S(f) was defined) and having
a bandwidth B
w
, then:
= 10log
10
2
2
This integral can be computed for a few "interesting" filter bandwidths, yielding filter losses
of 0.44 dB, 1.11 dB, and 3.31 dB when B
w
is 2/T
o
, 1/T
o
, and 1/2T
o
respectively. These
three example bandwidths correspond to
filters that pass the entire main frequency lobe,
half of that lobe, and one quarter of it.
You can experimentally verify these results using the RVP900 as follows:
• Using the Mt0 command, setup a T
o
= 0.5 μsec trigger pulse from the RVP900 in the
vicinity of range zero, and use that trigger to gate a signal generator whose output is
applied to the IFRD Burst Input. Also setup 125 m range resolution, and a rather long
6.0 μsec impulse response length. The long length makes the transition edges of the
matched
filter as steep as possible, so that it becomes a reasonably good
approximation to the ideal band pass filter used in the above analysis.
• Use the Pb command to verify that the burst pulse is present, and position the triggers
left and right until the pulse is centered exactly at zero.
Chapter 6 – Plot-assisted Setups
145
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